I would like to know if it is OK to use the Wilcoxon matched-pairs signed rank test to find significant differences between two sets of ordinal data, pre and post intervention (number of subjects is 10).
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The first step in conducting the paired-samples Wilcoxon signed rank test is to subtract the values, one value from the other in the pair. Because of this, it seems to me, the values would have to be at least interval in nature. If the data were strictly ordinal, you wouldn't be able to subtract them.
To go a little bit down a rabbit hole: I suppose you could also have situation where the data aren't quite interval, but that the differences can be ordered. This would also work for the test. For example, let's say you are measuring education, and you have High School < Bachelor's < Master's < Ph.D. You might be able to order the differences between these levels without making them truly interval. So, you say "The difference between a Ph.D. and Master's is less than the difference the difference between a Master's and a Bachelor's. But the difference between a Bachelor's and High School is larger still." And so on.
answered Jun 23, 2018 at 20:53